Introduction to probability:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Belmont, Mass.
Athena Scientific
2002
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| Edition: | 2. print. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 416 S. graph. Darst. |
| ISBN: | 188652940x |
Staff View
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| 245 | 1 | 0 | |a Introduction to probability |c Dimitri P. Bertsekas and John N. Tsitsiklis |
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| 264 | 1 | |a Belmont, Mass. |b Athena Scientific |c 2002 | |
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| 650 | 4 | |a Probabilités | |
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| 650 | 4 | |a Random variables | |
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Record in the Search Index
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| adam_text | Introduction to Probability
Dimitri P Bertsekas and John N Tsitsiklis
Massachusetts Institute of Technology
WWW site for book information and orders
http://wivAV athenasc com
Athena Scientific, Belmont, Massachusetts
Contents
1 Sample Space and Probability p 1
1 1 Sets p 3
1 2 Probabilistic Models p 6
1 3 Conditional Probability p 18
1 4 Total Probability Theorem and Bayes Rule p 28
1 5 Independence p 34
1 6 Counting p 43
1 7 Summary and Discussion p 50
Problems p 52
2 Discrete Random Variables p 71
2 1 Basic Concepts p 72
2 2 Probability Mass Functions p 74
2 3 Functions of Random Variables p 80
2 4 Expectation, Mean, and Variance p 81
2 5 Joint PMFs of Multiple Random Variables p 92
2 6 Conditioning p 98
2 7 Independence p 110
2 8 Summary and Discussion p 116
Problems p 119
3 General Random Variables p 139
3 1 Continuous Random Variables and PDFs p 140
3 2 Cumulative Distribution Functions p 148
3 3 Normal Random Variables p 152
3 4 Conditioning on an Event p 158
3 5 Multiple Continuous Random Variables p 164
3 6 Derived Distributions p 179
3 7 Summary and Discussion p 190
Problems p 192
vi Contents
4 Further Topics on Random Variables p 209
4 1 Transforms p 210
4 2 Sums of Independent Random Variables - Convolution p 221
4 3 More on Conditional Expectation and Variance p 225
4 4 Sum of a Random Number of Independent Random Variables p 232
4 5 Covariance and Correlation p 236
4 6 Least Squares Estimation p 240
4 7 The Bivariate Normal Distribution p 247
4 8 Summary and Discussion p 255
Problems p 257
5 The Bernoulli and Poisson Processes p 271
5 1 The Bernoulli Process p 273
5 2 The Poisson Process p 285
5 3 Summary and Discussion p 299
Problems p 301
6 Markov Chains p 313
6 1 Discrete-Time Markov Chains p 314
6 2 Classification of States p 321
6 3 Steady-State Behavior p 326
6 4 Absorption Probabilities and Expected Time to Absorption p 337
6 5 Continuous-Time Markov Chains p 344
6 6 Summary and Discussion p 352
Problems p 354
7 Limit Theorems p 379
7 1 Markov and Chebyshev Inequalities p 381
7 2 The Weak Law of Large Numbers p 383
7 3 Convergence in Probability p 386
7 4 The Central Limit Theorem p 388
7 5 The Strong Law of Large Numbers p 395
7 6 Summary and Discussion p 397
Problems p 399
Index p 411
|
| adam_txt |
Introduction to Probability
Dimitri P Bertsekas and John N Tsitsiklis
Massachusetts Institute of Technology
WWW site for book information and orders
http://wivAV athenasc com
Athena Scientific, Belmont, Massachusetts
Contents
1 Sample Space and Probability p 1
1 1 Sets p 3
1 2 Probabilistic Models p 6
1 3 Conditional Probability p 18
1 4 Total Probability Theorem and Bayes' Rule p 28
1 5 Independence p 34
1 6 Counting p 43
1 7 Summary and Discussion p 50
Problems p 52
2 Discrete Random Variables p 71
2 1 Basic Concepts p 72
2 2 Probability Mass Functions p 74
2 3 Functions of Random Variables p 80
2 4 Expectation, Mean, and Variance p 81
2 5 Joint PMFs of Multiple Random Variables p 92
2 6 Conditioning p 98
2 7 Independence p 110
2 8 Summary and Discussion p 116
Problems p 119
3 General Random Variables p 139
3 1 Continuous Random Variables and PDFs p 140
3 2 Cumulative Distribution Functions p 148
3 3 Normal Random Variables p 152
3 4 Conditioning on an Event p 158
3 5 Multiple Continuous Random Variables p 164
3 6 Derived Distributions p 179
3 7 Summary and Discussion p 190
Problems p 192
vi Contents
4 Further Topics on Random Variables p 209
4 1 Transforms p 210
4 2 Sums of Independent Random Variables - Convolution p 221
4 3 More on Conditional Expectation and Variance p 225
4 4 Sum of a Random Number of Independent Random Variables p 232
4 5 Covariance and Correlation p 236
4 6 Least Squares Estimation p 240
4 7 The Bivariate Normal Distribution p 247
4 8 Summary and Discussion p 255
Problems p 257
5 The Bernoulli and Poisson Processes p 271
5 1 The Bernoulli Process p 273
5 2 The Poisson Process p 285
5 3 Summary and Discussion p 299
Problems p 301
6 Markov Chains p 313
6 1 Discrete-Time Markov Chains p 314
6 2 Classification of States p 321
6 3 Steady-State Behavior p 326
6 4 Absorption Probabilities and Expected Time to Absorption p 337
6 5 Continuous-Time Markov Chains p 344
6 6 Summary and Discussion p 352
Problems p 354
7 Limit Theorems p 379
7 1 Markov and Chebyshev Inequalities p 381
7 2 The Weak Law of Large Numbers p 383
7 3 Convergence in Probability p 386
7 4 The Central Limit Theorem p 388
7 5 The Strong Law of Large Numbers p 395
7 6 Summary and Discussion p 397
Problems p 399
Index p 411 |
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| isbn | 188652940x |
| language | English |
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| physical | IX, 416 S. graph. Darst. |
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| spelling | Bertsekas, Dimitri P. 1942- Verfasser (DE-588)171165519 aut Introduction to probability Dimitri P. Bertsekas and John N. Tsitsiklis 2. print. Belmont, Mass. Athena Scientific 2002 IX, 416 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Probabilités Probabilités - Problèmes et exercices Probabilities Random variables Stochastic processes Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s b DE-604 Tsitsiklis, John N. 1958- Sonstige (DE-588)170583996 oth HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014175330&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bertsekas, Dimitri P. 1942- Introduction to probability Probabilités Probabilités - Problèmes et exercices Probabilities Random variables Stochastic processes Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4079013-7 |
| title | Introduction to probability |
| title_auth | Introduction to probability |
| title_exact_search | Introduction to probability |
| title_exact_search_txtP | Introduction to probability |
| title_full | Introduction to probability Dimitri P. Bertsekas and John N. Tsitsiklis |
| title_fullStr | Introduction to probability Dimitri P. Bertsekas and John N. Tsitsiklis |
| title_full_unstemmed | Introduction to probability Dimitri P. Bertsekas and John N. Tsitsiklis |
| title_short | Introduction to probability |
| title_sort | introduction to probability |
| topic | Probabilités Probabilités - Problèmes et exercices Probabilities Random variables Stochastic processes Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Probabilités Probabilités - Problèmes et exercices Probabilities Random variables Stochastic processes Wahrscheinlichkeitstheorie |
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